Finite Group Databasebeta

← #14759523

Subgroups — #14759523

Order 2816.

1476 conjugacy classes of subgroups.

The subgroup lattice has 810 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic, complemented
2C2×#10622777C211yesmaximal, characteristic, complemented
3C2×D8×Dic11C211yesmaximal, characteristic, complemented
4#13071311C211yesmaximal, characteristic, complemented
5#13068973C211yesmaximal, characteristic, complemented
6#13068966C211yesmaximal, characteristic, complemented
7#13068934C211yesmaximal, characteristic, complemented
8#13068872C211yesmaximal, characteristic, complemented
9#13068865C211yesmaximal, characteristic, complemented
10#13068806C211yesmaximal, characteristic, complemented
11#13068556C211yesmaximal, characteristic, complemented
12#13068443C211yesmaximal, characteristic, complemented
13#103×Dic11C211yesmaximal, characteristic, complemented
14#13068384C211yesmaximal, characteristic, complemented
15C2×C11×#449C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×D8C2211yescharacteristic
19C2×C11×#121C2211yescharacteristic
20#10623358—24no—
21#10623358—24no—
22C2×Q8×Dic11C2211yescharacteristic
23C2×Q8×Dic11C2211yescharacteristic
24C2×D4×Dic11—21no—
25C2×D4×Dic11—21no—
26C2×D4×Dic11C2211yescharacteristic
27C2×D4×Dic11C2211yescharacteristic
28C2×D4×Dic11C2211yescharacteristic
29C2×#66979—21no—
30C2×#66979C2211yescharacteristic
31C22×C4⋊Dic11—21no—
32C22×C4⋊Dic11C2211yescharacteristic
33C11×#449C418yescomplemented
34C2×C11×#103C2211yescharacteristic
35C2×C11×#102C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39#10622834—21no—
40#10622834C2211yescharacteristic
41#10622833—21no—
42C2×#66896C2211yescharacteristic
43C2×#66896C2211yescharacteristic
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46#10622825C2211yescharacteristic
47C2×C22⋊(C11⋊C8)C2211yescharacteristic
48#10622777—24no—
49D8×Dic11—24no—
50C2×#66882C2211yescharacteristic
51C2×#66882C2211yescharacteristic
52C2×#66879C2211yescharacteristic
53C2×C8×Dic11C2211yescharacteristic
54#10622598C2211yescharacteristic
55C4⋊C4×Dic11C2211yescharacteristic
56#10622564—21no—
57#10622563—21no—
58#10622189C2211yescharacteristic
59#10622189C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C2×C11×#41—22no—
65C2×C11×#41—22no—
66C2×C11×#41—22no—
67C2×C11×#41—22no—
68C2×C11×#41—22no—
69C2×C11×#41C2×C414yescomplemented
70C22×Q8×C11C2311yescharacteristic
71C22×D4×C11—21no—
72C22×D4×C11—21no—
73C22×D4×C11C2311yescharacteristic
74C22×D4×C11C2311yescharacteristic
75C23×C4×C11—21no—
76C23×C4×C11C2311yescharacteristic
77C23×Dic11—21no—
78C23×Dic11—21no—
79C23×Dic11—21no—
80C23×Dic11—21no—
81C2×C11×SD16—22no—
82C2×C11×SD16—22no—
83C2×C11×SD16C2×C414yescomplemented
84C2×C11×D8—22no—
85C2×C11×D8—22no—
86C2×C11×D8C2×C414yescomplemented
87C22×C8×C11C2311yescharacteristic
88C22×C8×C11C2311yescharacteristic
89C11×#121—22no—
90C11×#121C2×C414yescomplemented
91C2×C11×C4⋊C4C2311yescharacteristic
92C2×C11×C22⋊C4—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11—21no—
98C2×C22⋊Dic11—21no—
99C2×C22⋊Dic11D411yescharacteristic
100C2×C22⋊Dic11D411yescharacteristic
101Q8×Dic11—22no—
102Q8×Dic11—22no—
103Q8×Dic11—22no—
104Q8×Dic11D414yescomplemented
105D4×Dic11—28no—
106D4×Dic11—28no—
107D4×Dic11—22no—
108D4×Dic11—22no—
109D4×Dic11—22no—
110D4×Dic11—22no—
111D4×Dic11—22no—
112D4×Dic11D414yescomplemented
113#66979—28no—
114#66979—22no—
115#66979—22no—
116C2×C4⋊Dic11—28no—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—22no—
121C2×C4⋊Dic11—22no—
122C2×C4⋊Dic11—21no—
123C2×C4⋊Dic11D411yescharacteristic
124C2×C4⋊Dic11D411yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126C2×C4⋊Dic11C2311yescharacteristic
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131C2×C4×Dic11—21no—
132C2×C4×Dic11C2311yescharacteristic
133C2×C4×Dic11C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135C22×C11⋊C8C2311yescharacteristic
136C11×#103C2×C414yescomplemented
137C11×#102C2×C414yescomplemented
138C11×C22⋊C8C2×C414yescomplemented
139#66899—22no—
140#66899—22no—
141#66896—22no—
142#66896—22no—
143#66896—22no—
144#66896—22no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C22⋊(C11⋊C8)—22no—
149#66882—22no—
150#66882—22no—
151#66879—22no—
152C8×Dic11—22no—
153#21460—111nomaximal, Sylow
154C24×C11—21no—
155C24×C11—21no—
156C24×C11C2×D411yescharacteristic
157C11×#41—28no—
158C11×#41—28no—
159C11×#41—28no—
160C11×#41—28no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11C22×C412yes—
165C2×Q8×C11C2×D412yes—
166C2×Q8×C11#4112yes—
167C2×D4×C11—24no—
168C2×D4×C11—24no—
169C2×D4×C11—24no—
170C2×D4×C11—24no—
171C2×D4×C11—21no—
172C2×D4×C11—21no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—21no—
177C2×D4×C11—21no—
178C2×D4×C11—21no—
179C2×D4×C11—81no—
180C2×D4×C11—81no—
181C2×D4×C11C22×C412yes—
182C2×D4×C11C22×C412yes—
183C2×D4×C11C2×D412yes—
184C2×D4×C11#4112yes—
185C22×C4×C11—24no—
186C22×C4×C11—24no—
187C22×C4×C11—21no—
188C22×C4×C11—24no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11#4112yes—
197C22×C4×C11C2411yescharacteristic
198C22×Dic11—24no—
199C22×Dic11—24no—
200C22×Dic11—24no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—42no—
206C22×Dic11—81no—
207C22×Dic11—81no—
208C22×Dic11—81no—
209C22×Dic11—81no—
210C22×Dic11—81no—
211C22×Dic11—81no—
212C22×Dic11—81no—
213C22×Dic11—81no—
214C22×Dic11C2×D411yescharacteristic
215C22×Dic11C2×D411yescharacteristic
216C22×Dic11C2×D411yescharacteristic
217C22×Dic11C2×D411yescharacteristic
218C11×SD16—28no—
219C11×D8—28no—
220C2×C8×C11—21no—
221C2×C8×C11—21no—
222C2×C8×C11—21no—
223C2×C8×C11—21no—
224C2×C8×C11C22×C412yes—
225C2×C8×C11C22×C412yes—
226C11×C4⋊C4—21no—
227C11×C4⋊C4C22×C412yes—
228C11×C22⋊C4—24no—
229C22⋊Dic11—24no—
230C22⋊Dic11—22no—
231C22⋊Dic11—22no—
232C22⋊Dic11—24no—
233C22⋊Dic11—42no—
234C22⋊Dic11—81no—
235C22⋊Dic11—81no—
236C22⋊Dic11—81no—
237C4⋊Dic11—24no—
238C4⋊Dic11—24no—
239C4⋊Dic11—22no—
240C4⋊Dic11—24no—
241C4⋊Dic11—22no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—81no—
249C4⋊Dic11C2×D412yes—
250C4⋊Dic11C2×D412yes—
251C4×Dic11—24no—
252C4×Dic11—24no—
253C4×Dic11—21no—
254C4×Dic11—21no—
255C4×Dic11—81no—
256C4×Dic11C2×D412yes—
257C4×Dic11C2×D412yes—
258C2×C11⋊C8—21no—
259C2×C11⋊C8—21no—
260C2×C11⋊C8—21no—
261C2×C11⋊C8—21no—
262C2×C11⋊C8—21no—
263C2×C11⋊C8—21no—
264C2×#520—111no—
265C2×#449D1111yescharacteristic
266C2×#440—111no—
267C2×C4×D8—111no—
268#2324—111no—
269#1880—111no—
270#1879—111no—
271#1874—111no—
272#1863—111no—
273#1862—111no—
274#1852—111no—
275#1788—111no—
276#1762—111no—
277C4×#103—111no—
278#1750—111no—
279C23×C11—22no—
280C23×C11—21no—
281C23×C11—22no—
282C23×C11—21no—
283C23×C11—22no—
284C23×C11—21no—
285C23×C11—21no—
286C23×C11—21no—
287C23×C11—21no—
288C23×C11—22no—
289C23×C11—41no—
290C23×C11—41no—
291C23×C11—41no—
292C23×C11—41no—
293C23×C11—41no—
294C23×C11—41no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11C4×D412yes—
300C23×C11C22×D411yescharacteristic
301Q8×C11—22no—
302Q8×C11—22no—
303Q8×C11—22no—
304Q8×C11C4×D414yes—
305D4×C11—216no—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—22no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—84no—
314D4×C11C4×D414yes—
315C2×C4×C11—216no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—21no—
319C2×C4×C11—21no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—41no—
327C2×C4×C11—41no—
328C2×C4×C11C4×D412yes—
329C2×C4×C11C23×C411yescharacteristic
330C2×C4×C11C22×D411yescharacteristic
331C2×C4×C11C22×D411yescharacteristic
332C2×C4×C11C2×#4111yescharacteristic
333C2×C4×C11C2×#4111yescharacteristic
334C2×C4×C11C2×#4111yescharacteristic
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—21no—
344C2×Dic11—21no—
345C2×Dic11—21no—
346C2×Dic11—21no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11—41no—
351C2×Dic11—41no—
352C2×Dic11—41no—
353C2×Dic11—41no—
354C2×Dic11—41no—
355C2×Dic11—41no—
356C2×Dic11—41no—
357C2×Dic11—84no—
358C2×Dic11—84no—
359C2×Dic11—84no—
360C2×Dic11—84no—
361C2×Dic11#12012yes—
362C2×Dic11#12012yes—
363C8×C11—22no—
364C8×C11—22no—
365C11⋊C8—41no—
366C11⋊C8—41no—
367C22×#41C2×D1111yescharacteristic
368C22×SD16C2×D1111yescharacteristic
369C22×D8C2×D1111yescharacteristic
370C2×#121C2×D1111yescharacteristic
371#520—224no—
372#520—224no—
373C2×C4×Q8—111no—
374C2×C4×Q8—111no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×C4×D4—111no—
378C2×C4×D4—221no—
379C2×C4×D4—221no—
380C2×#117—111no—
381C2×#117—221no—
382C22×C4⋊C4—111no—
383C22×C4⋊C4—221no—
384#449Dic1118yescomplemented
385#440—224no—
386C4×D8—224no—
387C2×#107—111no—
388C2×#107—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#103C2×D1111yescharacteristic
392C2×#102—111no—
393C2×#102—111no—
394C2×#102—111no—
395C2×#102—111no—
396C2×#102C2×D1111yescharacteristic
397C2×C22⋊C8—111no—
398C2×C22⋊C8C2×D1111yescharacteristic
399C2×#97—111no—
400C2×C4×C8—111no—
401#390—111no—
402#390—221no—
403#389—111no—
404#388—221no—
405#386—221no—
406#385—221no—
407#380—111no—
408C4×C4⋊C4—111no—
409#340—111no—
410#340—111no—
411#340—111no—
412#340—111no—
413#336—111no—
414#336—111no—
415C22×C11—22no—
416C22×C11—22no—
417C22×C11—22no—
418C22×C11—24no—
419C22×C11—41no—
420C22×C11—42no—
421C22×C11—41no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—42no—
425C22×C11—41no—
426C22×C11—42no—
427C22×C11—41no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—81no—
433C22×C11—81no—
434C22×C11—81no—
435C22×C11—81no—
436C22×C11C2×C4×D411yescharacteristic
437C22×C11C2×#12011yescharacteristic
438C22×C11#52511yescharacteristic
439C22×C11#57611yescharacteristic
440C22×C11#57611yescharacteristic
441C22×C11#57711yescharacteristic
442C22×C11#57811yescharacteristic
443C4×C11—22no—
444C4×C11—24no—
445C4×C11—42no—
446C4×C11C2×C4×D411yescharacteristic
447C4×C11C2×C4×D411yescharacteristic
448C4×C11#52511yescharacteristic
449C4×C11#52511yescharacteristic
450Dic11—22no—
451Dic11—22no—
452Dic11—41no—
453Dic11—42no—
454Dic11—42no—
455Dic11—41no—
456Dic11—81no—
457Dic11—81no—
458C2×#41—22no—
459C2×#41—22no—
460C2×#41—22no—
461C2×#41—22no—
462C2×#41—22no—
463C2×#41C2×Dic1114yescomplemented
464C22×Q8C22×D1111yescharacteristic
465C22×D4—21no—
466C22×D4—21no—
467C22×D4C22×D1111yescharacteristic
468C22×D4C22×D1111yescharacteristic
469C23×C4—21no—
470C23×C4—221no—
471C23×C4—221no—
472C23×C4—221no—
473C23×C4—221no—
474C23×C4C22×D1111yescharacteristic
475C2×SD16—22no—
476C2×SD16—22no—
477C2×SD16C2×Dic1114yescomplemented
478C2×D8—22no—
479C2×D8—22no—
480C2×D8C2×Dic1114yescomplemented
481C22×C8—111no—
482C22×C8—111no—
483C22×C8C22×D1111yescharacteristic
484C22×C8C22×D1111yescharacteristic
485#121—22no—
486#121C2×Dic1114yescomplemented
487C4×Q8—114no—
488C4×Q8—222no—
489C4×Q8—222no—
490C4×Q8—222no—
491C4×D4—114no—
492C4×D4—222no—
493C4×D4—222no—
494C4×D4—222no—
495C4×D4—222no—
496C4×D4—228no—
497C4×D4—228no—
498C4×D4—222no—
499#117—222no—
500#117—222no—
501#117—228no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—111no—
504C2×C4⋊C4—111no—
505C2×C4⋊C4—111no—
506C2×C4⋊C4—111no—
507C2×C4⋊C4—111no—
508C2×C4⋊C4—222no—
509C2×C4⋊C4—222no—
510C2×C4⋊C4—221no—
511C2×C4⋊C4—221no—
512C2×C4⋊C4—228no—
513C2×C4⋊C4—221no—
514C2×C4⋊C4—221no—
515C2×C4⋊C4C22×D1111yescharacteristic
516C2×C22⋊C4—21no—
517C2×C22⋊C4—111no—
518C2×C22⋊C4—111no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C22⋊C4—221no—
523C2×C22⋊C4—221no—
524C2×C22⋊C4—221no—
525C2×C42—111no—
526C2×C42—111no—
527C2×C42—221no—
528C2×C42—221no—
529C2×C42—221no—
530#107—222no—
531#107—222no—
532#103—222no—
533#103—222no—
534#103C2×Dic1114yescomplemented
535#102—222no—
536#102—222no—
537#102—222no—
538#102—222no—
539#102C2×Dic1114yescomplemented
540C22⋊C8—222no—
541C22⋊C8C2×Dic1114yescomplemented
542#97—222no—
543C4×C8—222no—
544#95—221no—
545#95—221no—
546#95—221no—
547C2×C11—42no—
548C2×C11—44no—
549C2×C11—82no—
550C2×C11C4×#12011yescharacteristic
551C2×C11#294611yescharacteristic
552C2×C11#295111yescharacteristic
553C2×C11#300811yescharacteristic
554C2×C11#301311yescharacteristic
555C2×C11#311911yescharacteristic
556C2×C11#312411yescharacteristic
557C24—21no—
558C24—21no—
559C24D4×D1111yescharacteristic
560#41—28no—
561#41—28no—
562#41—28no—
563#41—28no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8—21no—
567C2×Q8D4×D1112yes—
568C2×Q8#434112yes—
569C2×Q8C22×Dic1112yes—
570C2×D4—24no—
571C2×D4—24no—
572C2×D4—24no—
573C2×D4—24no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4D4×D1112yes—
585C2×D4#434112yes—
586C2×D4C22×Dic1112yes—
587C2×D4C22×Dic1112yes—
588C22×C4—24no—
589C22×C4—24no—
590C22×C4—21no—
591C22×C4—24no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—224no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—224no—
605C22×C4—224no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—442no—
609C22×C4—881no—
610C22×C4—881no—
611C22×C4—881no—
612C22×C4—881no—
613C22×C4—881no—
614C22×C4—881no—
615C22×C4—881no—
616C22×C4—881no—
617C22×C4D4×D1111yescharacteristic
618C22×C4#434112yes—
619C22×C4C22×Dic1112yes—
620C22×C4C23×D1111yescharacteristic
621SD16—28no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—221no—
628C2×C8—221no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8C22×Dic1112yes—
634C2×C8C22×Dic1112yes—
635C4⋊C4—21no—
636C4⋊C4—112no—
637C4⋊C4—112no—
638C4⋊C4—222no—
639C4⋊C4—222no—
640C4⋊C4—224no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4—221no—
646C4⋊C4—221no—
647C4⋊C4—221no—
648C4⋊C4—221no—
649C4⋊C4—881no—
650C4⋊C4C22×Dic1112yes—
651C22⋊C4—24no—
652C22⋊C4—222no—
653C22⋊C4—222no—
654C22⋊C4—224no—
655C22⋊C4—224no—
656C22⋊C4—442no—
657C22⋊C4—881no—
658C22⋊C4—881no—
659C22⋊C4—881no—
660C42—112no—
661C42—112no—
662C42—224no—
663C42—224no—
664C42—221no—
665C42—221no—
666C42—881no—
667C11#2146011yescharacteristic, complemented, Sylow
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—22no—
673C23—21no—
674C23—22no—
675C23—21no—
676C23—22no—
677C23—22no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23D4×Dic1112yes—
689C23C2×D4×D1111yescharacteristic
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8D4×Dic1114yes—
694D4—216no—
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—41no—
701D4—41no—
702D4—84no—
703D4D4×Dic1114yes—
704C2×C4—216no—
705C2×C4—22no—
706C2×C4—21no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—112no—
718C2×C4—112no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—221no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—221no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—884no—
742C2×C4—884no—
743C2×C4—884no—
744C2×C4—884no—
745C2×C4D4×Dic1112yes—
746C2×C4C2×D4×D1111yescharacteristic
747C2×C4C2×D4×D1111yescharacteristic
748C2×C4C2×#434111yescharacteristic
749C2×C4C2×#434111yescharacteristic
750C2×C4C2×#434111yescharacteristic
751C2×C4C23×Dic1111yescharacteristic
752C8—22no—
753C8—22no—
754C8—441no—
755C8—441no—
756C22—22no—
757C22—24no—
758C22—22no—
759C22—22no—
760C22—41no—
761C22—42no—
762C22—41no—
763C22—42no—
764C22—41no—
765C22—42no—
766C22—41no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—42no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22#1062311711yescharacteristic
778C22D11×#12011yescharacteristic
779C22#1062330011yescharacteristic
780C22#1062330211yescharacteristic
781C22#1062330511yescharacteristic
782C22#1062330611yescharacteristic
783C22C2×D4×Dic1111yescharacteristic
784C4—22no—
785C4—24no—
786C4—42no—
787C4—222no—
788C4—222no—
789C4—441no—
790C4—442no—
791C4—442no—
792C4—441no—
793C4—881no—
794C4—881no—
795C4#1062311711yescharacteristic
796C4#1062311711yescharacteristic
797C4C2×D4×Dic1111yescharacteristic
798C4C2×D4×Dic1111yescharacteristic
799C2—42no—
800C2—44no—
801C2—82no—
802C2#120×Dic1111yescharacteristic
803C2#1307744911yescharacteristic
804C2#1307749211yescharacteristic
805C2#1307788111yescharacteristic
806C2#1307792911yescharacteristic
807C2#1307880811yescharacteristic
808C2#1307887111yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC2×C11×#449C2
socleC23×C11C22×D4
cosocleC22×C4×C11C24
hypercenterC2×#449D11
hypocenterC11#21460
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#449

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#10623358C2semidirect
2. C2×#10622777C2semidirect
3. C2×D8×Dic11C2semidirect
4. #13071311C2semidirect
5. #13068973C2semidirect
6. #13068966C2semidirect
7. #13068934C2semidirect
8. #13068872C2semidirect
9. #13068865C2semidirect
10. #13068806C2semidirect
11. #13068556C2semidirect
12. #13068443C2semidirect
13. #103×Dic11C2semidirect
14. #13068384C2semidirect
33. C11×#449C4semidirect
69. C2×C11×#41C2×C4semidirect
83. C2×C11×SD16C2×C4semidirect
86. C2×C11×D8C2×C4semidirect
90. C11×#121C2×C4semidirect
104. Q8×Dic11D4semidirect
112. D4×Dic11D4semidirect
136. C11×#103C2×C4semidirect
137. C11×#102C2×C4semidirect
138. C11×C22⋊C8C2×C4semidirect
384. #449Dic11semidirect
463. C2×#41C2×Dic11semidirect
477. C2×SD16C2×Dic11semidirect
480. C2×D8C2×Dic11semidirect
486. #121C2×Dic11semidirect
534. #103C2×Dic11semidirect
539. #102C2×Dic11semidirect
541. C22⋊C8C2×Dic11semidirect
667. C11#21460semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#106233582
C2×#106227772
C2×D8×Dic112
#130713112
#130689732
#130689662
#130689342
#130688722
#130688652
#130688062
#130685562
#130684432
#103×Dic112
#130683842
C2×C11×#4492
#2146011